Given the following graph of h(x), identify:
1. The intervals where h(x) is increasing and decreasing.
2. The local maximum and minimum points of h(x)
3. The intervals where h(x) is concave up and concave down
4. The inflection point
5. Sketch the graph of h'(x) and h''(x).
The Attempt at a Solution
I know I drew the graph really bad, but from my book the slope is 0 at x = 2. So the intervals of increase would be when x < 2 and x > 2, but what about the decrease since there is no negative slope at all? How would I determine the local maximums and local minimums in this scenario seeing as there is no decrease to a negative slope? What would be the inflection point in this case, if there aren't any local maximums and local minimums? Normally, I wouldn't have trouble drawing the derivative of this graph. However, it is a 3rd degree polynomial which would mean the derivative would be a parabola. How could I draw a parabola with only one value for x?
Any help? Thanks in advance.